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Question

A 5m long cylindrical steel wire with radius 2×103m is suspended vertically from a rigid support and carries a bob of mass 100 kg at the other end. If the bob gets snapped, calculate the change in temperature of the wire ignoring radiation losses.
(For the steel wire: Youngs Modulus =2.1×1011Pa; Density =7860kg/m3; Specific heat =420 J/kg-K).

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Solution

msΔθ=ΔU=(1/2)× stress ×strain × volume
(A.L.ρ)sΔθ=(Mg)2L/(2YA) neglecting the strain due to the weight of wire
Δθ=(Mg)2/(2ρAYs)=0.00457 K.

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